Thanks @robroy for that link. However it's unclear to me how that would help me in SSHing into the odroid. The article talks about "transmitting data", please correct me if I am wrong, but that wouldn't allow me access to a linux terminal like SSH does, right?

The following is in reference to the Beaglebone -

This lead can server the dual purpose of both supplying power to the BBB and allowing the BBB toemulate a USB modem. It is this trick that allows the BBB to be accessed as if it were networked,allowing you to communicate with it using a browser or SSH client on your computer.

That's what I am trying to achieve with the Odroid. Based on that, could you clarify on the steps again and whether your article is still relevant or not?

And I don't wish to use any external peripherals like the USB-UART connector.

You need a HDMI monitor at least to test the gadget driver functionality.Robroy's link explains the gadget driver (ethernet over usb) configuration.If it works, you can add the settings into init rc sys or systemd for the auto-start.